Influential cleric Moqtada al-Sadr and Iran backed Nuri-al-Maliki are locked in a tussle to gain enough power before the upcoming elections.
ISIS claimed a series of suicide attacks that killed at least 14 people south and west of Baghdad on Monday.
ISIS’s assault on Kirkuk, which lies in an oil-producing region, killed six members of the security forces and two Iranians
The battle in Falluja has allowed Abadi to shift the focus domestically away from a crisis that unfolded when he failed to push through a cabinet reshuffle he sought as part of his drive to fight corruption.
The assault on Falluja has begun what is expected to be one of the biggest battles ever fought against Islamic State. About 50,000 civilians remain in the city, according to the United Nations.